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# A student’s average score for 10 tests was x. The grader then discover

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Math Expert
Joined: 02 Sep 2009
Posts: 58458
A student’s average score for 10 tests was x. The grader then discover  [#permalink]

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21 Jan 2019, 00:09
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Difficulty:

25% (medium)

Question Stats:

80% (00:40) correct 20% (00:14) wrong based on 19 sessions

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A student’s average score for 10 tests was x. The grader then discovered that there was an error on two of the tests. On one of the tests, the student’s score should have been 10 points lower. On another test, the student’s score should have been 20 points higher. After the grader corrects these mistakes, what is the student’s new average, in terms of x?

A x – 1
B x
C x + 1
D x + 10
E x + 20

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Joined: 09 Mar 2018
Posts: 994
Location: India
Re: A student’s average score for 10 tests was x. The grader then discover  [#permalink]

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21 Jan 2019, 00:19
Bunuel wrote:
A student’s average score for 10 tests was x. The grader then discovered that there was an error on two of the tests. On one of the tests, the student’s score should have been 10 points lower. On another test, the student’s score should have been 20 points higher. After the grader corrects these mistakes, what is the student’s new average, in terms of x?

A x – 1
B x
C x + 1
D x + 10
E x + 20

So 10 tests, average => Total initial sum / 10 = x --------------(a)

Error in 2 tests, will mean that from original sum, we will subtract 10 and add 20, This will make the changed sum as, Total Initial sum + 10

New average =$$\frac{{Total Initial sum + 10}}{10}$$, Using (a)
x + 1

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Joined: 31 Oct 2013
Posts: 1464
Concentration: Accounting, Finance
GPA: 3.68
WE: Analyst (Accounting)
Re: A student’s average score for 10 tests was x. The grader then discover  [#permalink]

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21 Jan 2019, 04:34
Bunuel wrote:
A student’s average score for 10 tests was x. The grader then discovered that there was an error on two of the tests. On one of the tests, the student’s score should have been 10 points lower. On another test, the student’s score should have been 20 points higher. After the grader corrects these mistakes, what is the student’s new average, in terms of x?

A x – 1
B x
C x + 1
D x + 10
E x + 20

average of 10 tests = x

Total = 10x

correction = 10x + 20 -10 = 10x + 10.

New Total = 10x + 10.

New average = 10x + 10 / 10 = x + 1.

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Joined: 18 Aug 2017
Posts: 5017
Location: India
Concentration: Sustainability, Marketing
GPA: 4
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Re: A student’s average score for 10 tests was x. The grader then discover  [#permalink]

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21 Jan 2019, 07:59
Bunuel wrote:
A student’s average score for 10 tests was x. The grader then discovered that there was an error on two of the tests. On one of the tests, the student’s score should have been 10 points lower. On another test, the student’s score should have been 20 points higher. After the grader corrects these mistakes, what is the student’s new average, in terms of x?

A x – 1
B x
C x + 1
D x + 10
E x + 20

new score : x-10+8x+x+10
=> 10x+10
avg of new sum
10x+10/ 10
= x+1
IMO C
Re: A student’s average score for 10 tests was x. The grader then discover   [#permalink] 21 Jan 2019, 07:59
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